Not many grocery stores can claim cult followings, certainly not in Brooklyn, where the only options in some neighborhoods tend to be oversize bodegas carrying expired goods or overpriced green grocers full of kale, quinoa and craft beer.

Wegmans, the family-owned, Rochester-based chain of 85 stores concentrated in the Great Lakes region and the Washington Beltway, has that kind of following, inspiring fan websites, hashtags, T-shirts, even a high school musical about a couple who finds love in the aisles. The company is poised to open its first New York City store, and it has selected one of the most ripe locations: the derelict Admiral’s Row at the Brooklyn Navy Yard.

After a decade of fighting over whether to save the Civil War-era homes of Admiral’s Row along Flushing Avenue, the Navy Yard’s board approved a deal for the redevelopment of the site on Tuesday. Several buildings will be knocked down and replaced with Wegmans, other stores, industrial space and parking. Steiner NYC, creator of the Navy Yard’s 25-acre film studio, will develop the complex, set to open in 2017.

To its devotees, Wegmans strikes the balance between the variety of a Whole Foods, the prices of a Trader Joe’s and the scale of a Walmart. The 74,000-square-foot store at the Navy Yard will be the company’s smallest by about 25 percent, but will still be about 20,000 square feet larger than the Fairway in Red Hook or the Whole Foods in Gowanus, two favorites of Brooklyn’s multimillion-dollar brownstone set.

Yet the affordable prices at Wegmans should also appeal to residents of nearby housing projects who have been clamoring for a supermarket for years. “We’ve got these high-priced, ritzy stores opening on all sides,” said Anthony Sosa, president of the Ingersoll Houses residents’ association. “People are feeling closed in and left out.”

Founded in 1916, Wegmans has consistently been ranked the top grocery store in the nation by Consumer Reports and the Food Network, and Forbes placed it among the top 10 employers in the country.

The Navy Yard selected Steiner and Wegmans above three other proposals because of the affordability of the store’s offerings and its commitment to hiring locally for full-time jobs, said David Ehrenberg, president of the Brooklyn Navy Yard Development Corporation, the city agency that runs the 300-acre industrial complex on the East River.

Because of its emphasis on prepared foods, the company offered to create at least twice as many full-time jobs (200), and more total jobs (600) than any of the rivals. In its first two weeks of hiring, the store will interview exclusively from the three housing projects that border the Navy Yard, a community it hopes will be on both sides of the checkout line, said Danny Wegman, the grocer’s third-generation chief executive.

“People need not just good food, but good jobs,” Mr. Wegman said. “Brooklyn provides an incredible opportunity for both.”

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The proposed Wegmans store, set to open in 2017, at the Brooklyn Navy Yard.CreditGreenbergFarrow

The Navy Yard was decommissioned by the federal government in the 1960s and later turned over to the city. Preservationists denounced the decision to redevelop the former quarters of the Navy Yard’s commanders, and in the end, two buildings were set aside for restoration, one of which will house 78,000 square feet of shops.

Across a large parking lot will be the supermarket, part of a larger building with 126,000 square feet of industrial space. Across Sands Street, a four-story parking garage will be built, for use by Wegmans and other Navy Yard tenants, with a floor or two of industrial space above it.

Steiner will pay for the construction, estimated to cost $140 million, and will collect rent from the businesses there, including Wegmans. In turn, Steiner has a 96-year lease paying the Navy Yard “above market rents,” Mr. Ehrenberg said, though he would not specify how much.

Some Fort Greene residents who grew up with Wegmans could not contain their excitement.

Samantha Kartanowicz’s jaw dropped when she heard one might soon open up near her apartment. “I was just saying this morning how we could use a really good grocery store around here,” she said, having frequented a Baltimore store as a child.

For Dan Kublick, a Syracuse native, there is no more reliable way to know when his friends have returned to their hometown. “They start posting photos from Wegmans on Instagram,” he said.

Correction:May 12, 2015

An earlier version of this article misstated the year Wegmans was founded. It was 1916, not 1917.

Correction:May 16, 2015

A picture caption in some editions on Wednesday with an article about plans to build a Wegmans grocery store at the Brooklyn Navy Yard carried an incorrect credit for a rendering of the store. It is by GreenbergFarrow, not Beyer Blinder Belle.

A version of this article appears in print on , Section A, Page 20 of the New York edition with the headline: Wegmans to Open First City Store at Brooklyn Navy Yard. Order Reprints | Today’s Paper | Subscribe